- #1
freshyy
- 5
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This is a general question that i am confused about. If I throw a ball up, then is the distance that it reaches at the very top the y or y-initial? Also, is this y or y-initial positive or negative?
In summary, the conversation discusses the use of coordinates in projectile motion problems and how to determine the height of a ball at its highest point. It also mentions the equation for calculating this height and clarifies that the time it takes for the ball to come down may not be twice the time it takes to reach its maximum height.
- #2
berkeman
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freshyy said:
You can define your coordinates however is the most convenient for solving any particular problem. The simplest 2-d coordinate system for projectile motion problems would be to put the origin on the ground, with the x-axis horizontal and the y-axis vertical. That means y=0 is at ground level, so if you are 6 feet tall and throw a ball up, then y(t=0)=6', and Vy(0)= whatever velocity you release the ball at time t=0. The height at the top of the ball's travel will depend on Vy(0) at the release point y(0)=6' plus however long it takes for the ball to stop moving up. Use an equation like this...
y(t) = y(0) + Vy(0)*t + 1/2*ay*t^2
Where a = the acceleration due to gravity, which in this case is -9.8m/s^2.
Does that help?
- #3
freshyy
- 5
- 1
berkeman said:
Yes, thank you
- #4
freshyy
- 5
- 1
berkeman said:
Also, the time that the ball takes to come down is twice the time the ball takes to reach its maximum height, right?
- #5
berkeman
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freshyy said:
Not if you release it from your 6' height. Right?
- #6
berkeman
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Well, I mean the two times from release to apex, and from apex to hitting the ground. Those are not equal.
- #7
freshyy
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- 1
Yea, in understand it now thank you.berkeman said:
1. What is the sign of y when a ball is thrown up?
The sign of y when a ball is thrown up depends on the direction of the ball's motion. If the ball is moving upwards, the sign of y is positive. If the ball is moving downwards, the sign of y is negative.
2. Does the sign of y change if the ball is thrown at an angle?
Yes, the sign of y can change if the ball is thrown at an angle. If the ball is thrown upwards at an angle, the sign of y will still be positive. However, if the ball is thrown downwards at an angle, the sign of y will be negative.
3. How does the sign of y affect the ball's trajectory?
The sign of y does not affect the ball's trajectory directly. It is simply a way to indicate the direction of the ball's motion along the y-axis. The ball's trajectory is primarily influenced by factors such as initial velocity, angle of throw, and gravity.
4. Can the sign of y change during the ball's flight?
Yes, the sign of y can change during the ball's flight. For example, if the ball reaches its highest point and begins to fall back down, the sign of y will change from positive to negative.
5. Is the sign of y important in determining the ball's position?
Yes, the sign of y is important in determining the ball's position along the y-axis. It helps us understand the direction of the ball's motion and can be used in equations to calculate its position at a specific time.
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